# Questions tagged [linear-systems]

A linear system operates on inputs with only linear operators so the response to a complex input can be analysed as the sum of the response to a set of simpler inputs. This mathematical property makes the analysis of linear systems much simpler than non-linear systems where this summation or superposition does not hold. Linear systems are generally further classified as time invariant, meaning that there characteristics do not change over time.

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### What is meant by a system's “impulse response” and “frequency response?”

Can anyone state the difference between frequency response and impulse response in simple English?
1answer
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5answers
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### Why Does the Kalman Filter Remove Only Gaussian Noise?

What and where in the derivation of the Kalman filter is the assumption of Gaussian noise? Why and how does this assumption help?
4answers
916 views

### Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
3answers
2k views

### How to Prove a System Is Invertible?

what i know is that for a system to be invertibel it should be one-one , but I am confused that if i am given a transfer function of a LTI system how can I prove or verify if it is invertible. ...
1answer
5k views

### Initial conditions for the LTI systems described as a difference equations

Why do we need the initial conditions to be zero for the LTI systems described as a difference equations? First question is why do we need it for linearity? I can't think of any example of the non ...
1answer
91 views

### Why not use the same “standard” exponentials for both continuous and discrete time

In continuous time the standard exponential signal is usually defined as $$e^{st}, \quad\text{with}\quad s = \sigma+j \omega$$ In discrete time the standard exponential signal is usually defined as ...
2answers
8k views

### Given the input and the output, how to determine the impulse response?

I would like to find the impulse response, $h[n]$, of an LTI system given the input $$x[n] = [1,-3,2]$$ and the output $$y[n] = [1,-1,-4,4]$$ I know that $y[t]=x[t]*h[t]$, but I am having hard ...
3answers
424 views

### Deconvolution (Linear Convolution) with an Under Determined System of Equations?

If I have a measured signal $\mathbf{y}$ which is the result of the true signal $\mathbf{x}$ convolved with another function (linear and not circular convolution), I always seem to get an ...
1answer
2k views

### Finding the Wiener filter transfer function

I am trying to understand the mechanism of finding the transfer function for a Wiener function. ...
1answer
3k views

### Does “improper” imply that a system cannot be stable and causal?

This answer and the comments in it made me wonder whether the following statement is true: If a transfer function is improper, then that system cannot be causal and stable at the same time. I had ...
1answer
353 views

### LTI system without constant coefficient differential equation

I have encountered a system where the output $y(t)$ and input $x(t)$ are related in the laplace domain as: $$Y(s) = H(s)X(s) \tag1$$ which is typical. However, $H(s)$ is not a rational function of ...
1answer
299 views

### Difference between convolving before/after discretizing LTI systems

Suppose I have transfer functions for two continuous causal linear-time invariant (LTI) systems: $F_1(s)$ and $F_2(s)$. Let $D\left\{\cdot\right\}$ denote the function that maps a transfer function ...
1answer
341 views

### How to perform model fitting for system identification

I am having a really hard time in understanding how to formulate a model say linear AR model to represent a communication channel or maybe any motion. I have the experimental data representing the ...
1answer
244 views

### ARMA (Auto Regressive Mean Average) Process Representation as AR (Auto Regressive)

Let's say we have an ARMA (Auto Regressive Moving Average Model) process where the transfer function is a minimum phase system (Namely Invertible). By Wold's Decomposition it is guaranteed to have MA ...